The present invention relates generally to segmentation masks resulting from nuclear magnetic resonance imaging and, in particular, relates to a method and apparatus for fitting a smooth boundary to a segmentation mask.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or xe2x80x9ctippedxe2x80x9d, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emited by the excited spins after the excitation signal B1 is terminated. This signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx Gy and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well-known reconstruction techniques.
The prognosis of patients with a wide variety of cardiac diseases, for example, has been closely linked to the performance of the heart as indicated by measurements such as wall thickening, wall motion, and myocardial mass. Accurate quantitative measures of regional contractile function could therefore have significant prognostic and therapeutic importance. For example, many patients with severe coronary artery disease may have normal regional and global left ventricular function at rest but have abnormalities induced by stress. In clinical practice, patients with coronary artery disease can be detected by stress echocardiography based on new functional deficits during stress. However, interobserver variability of this type of qualitative measure is an inherent limitation that could be improved with quantitative measures. Thus, there is a need for high quality quantitative measures of regional cardiac function.
Image data of the epicardial boundary, for example, is currently acquired by applying a specific sequence of RF pulses to yield a NMR signal that provides information pertaining to the tissue under test. A particular pulse sequence can therefore be applied to obtain an image of, for example, a cross-section of the left ventricle tissue.
Segmentation methods that are currently available include snake-based techniques such as that described by A. Yezzi, et al. xe2x80x9cA Geometric Snake Model for Segmentation of Medical Imagery,xe2x80x9d IEEE Transaction on Medical Imaging, 16, 199-209 (April, 1997). Snakes, also known as active contours, have been used in an attempt to segment features of the left ventricle. Snakes are described by a parameterized curve whose evolution is determined by the minimization of an energy field. The equation of the energy field, as defined by J. C. Gardner et al. xe2x80x9cA Semi-Automated Computerized System for Fracture Assessment of Spinal X-Ray Films,xe2x80x9d Proceedings of the International Society for Optical Engineering, 2710, 996-1008 (1996), is:                               E          ⁡                      [                                          x                →                            ⁡                              (                s                )                                      ]                          ≡                  k          ⁢                                    ∫              0              1                        ⁢                          xe2x80x83                        ⁢                          ⅆ                              s                ⁡                                  [                                                                                    1                        2                                            ⁢                                                                        α                          ⁡                                                      (                                                                                          ⅆ                                                                  x                                  →                                                                                                                            ⅆ                                s                                                                                      )                                                                          2                                                              +                                                                  1                        2                                            ⁢                                                                        β                          ⁡                                                      (                                                                                                                            ⅆ                                  2                                                                ⁢                                                                  x                                  →                                                                                                                            ⅆ                                                                  s                                  2                                                                                                                      )                                                                          2                                                              -                                          γ                      ⁢                                              xe2x80x83                                            ⁢                                              H                        ⁡                                                  (                                                                                    x                              →                                                        ⁡                                                          (                              s                              )                                                                                )                                                                                                      ]                                                                                        (        1        )            
where s is the parameterization variable, {right arrow over (x)} is the parameterized curve, xcexa is the normalization constant, xcex1 is the H({right arrow over (x)})=|{right arrow over (∇)}/({right arrow over (x)})| tension of the snake, xcex2 is the rigidity of the snake, xcex3 controls the attraction to image features, and I is the pixel intensity of the image. H (x) refers to a function which defines the features that attract the snake algorithm to the boundary and, typically, is chosen to be the magnitude of the gradient of the image intensity.
Because the magnitude of the gradient is used to attract the algorithm to the boundary of the left ventricle, the snake does not work well where the boundary is defined by edges that are weak in intensity. In order for the snake algorithm to attach to a boundary, a user must intervene and supply a boundary condition to define the proximity of the boundary for the snake. This is undesirable because user may need to interact with the segmentation algorithm while the images are being processed.
Snake based techniques can be used, as described by Yezzi, to produce a geometric snake model having a stopping term and a constant inflation term added to the evolution equation. The resulting evolution equation of the Yezzi active contour model is:                                           ∂            Ψ                                ∂            t                          =                              φ            ⁢                          "LeftBracketingBar"              "RightBracketingBar"                        ⁢                          ∇              Ψ                        ⁢                          "LeftBracketingBar"              "RightBracketingBar"                        ⁢                          (                              κ                +                v                            )                                +                                    ∇              φ                        *                          ∇              Ψ                                                          (        2        )            
where v is a constant inflation force,   κ  ≡      div    ⁡          (                        ∇          ψ                                      "LeftBracketingBar"            "RightBracketingBar"                    ⁢                      ∇            ψ                    ⁢                      "LeftBracketingBar"            "RightBracketingBar"                              )      
xe2x80x83the curvature of the level sets of "psgr"(x, y, t), xcfx86 is a function dependent on the type of image and is a stopping term for the curve evolution. Snake based techniques are additionally unfavorable because they rely primarily on edge information only, and therefore are subject to greater error and generally lack robustness, particularly in a clinical setting. S. Ranganath attempted unsuccessfully to segment an epicardium using a snake, as described in xe2x80x9cContour Extraction from Cardiac MRI Studies Using Snakes,xe2x80x9d IEEE Transactions on Medical Imaging, 14(2), 328-338 (June, 1995).
Another such method is disclosed herein with reference to pending U.S. patent application Ser. No. 09/652,739, filed by the present assignee and entitled xe2x80x9cMethod and Apparatus for Segmentation of a Left Ventricular Epicardium.xe2x80x9d The disclosure of the referenced pending application is hereby incorporated by reference.
When segmenting a left ventricular epicardium, as well as other internal body parts, it is typical to represent the area of interest with a binary mask. Pixels inside the area of interest are marked xe2x80x9conxe2x80x9d and pixels outside the area are marked xe2x80x9coff.xe2x80x9d Many times it is of interest to show the boundary of an organ or region that has been segmented. Conventional segmentation operations have been unsuccessful in producing an accurate representation of the boundary between the organ to be segmented and its surroundings. What is therefore needed is a method and apparatus for transforming a segmentation mask into a smooth, closed contour that is representative of the body part under examination.
The present invention relates to a method and apparatus for fitting a smooth boundary curve to a segmented image of a human organ or tissue.
In accordance with a first aspect of the invention, boundary points of a mask produced using, for example, a magnetic resonance imaging system each are at least partially defined by a corresponding radius. The length of each radius is compared to a predetermined interval, and those falling outside of the interval are removed. The remaining radii define corresponding remaining boundary points of the image. Next, a moving window encapsulates a portion of the remaining radii, which are then examined to determine whether a given radius falls within a second predetermined interval. Those radii falling outside of the predetermined interval are adjusted such that the adjusted lengths fall within the interval. The remaining boundary points are then curve fit to produce a smooth and continuous contour.